Isotropic collimation devices and related methods

ABSTRACT

Devices, such as light-emitting devices (e.g., LEDs), and methods associated with such devices are provided. A light-emitting device may include an interface through which emitted light passes therethrough. The interface having a dielectric function that varies spatially according to a pattern, wherein the pattern is arranged to provide light emission that has a substantially isotropic emission pattern and is more collimated than a Lambertian distribution of light.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Application Ser. No. 60/727,753, filed on Oct. 17, 2005, andU.S. Provisional Application Ser. No. 60/737,136, filed on Nov. 16,2005, which are herein incorporated by reference in their entirety.

FIELD OF INVENTION

The invention relates generally to light-emitting devices, as well asrelated components, systems, and methods, and more particularly tolight-emitting devices having patterned interfaces.

BACKGROUND

There are a variety of light-emitting devices, such as light-emittingdiodes (LEDs), laser diodes, and optical amplifiers, which can emitlight and which may be used in various applications. The emitted lightmay be characterized by numerous metrics, including light extraction,collimation, and azimuthal isotropy. Light extraction is a measure ofthe amount of light emitted as compared to the amount of light generatedwithin the light-emitting device. Collimation is a measure of theangular deviation of emitted light with respect to the normal of theemission surface of the light-emitting device. Azimuthal isotropy (oruniformity) is a measure of the uniformity of light emitted versus anazimuthal angle, hereafter sometimes referred to simply as isotropy.

Each of the above-mentioned metrics of a light-emitting device may playan important role in determining the suitability of a particularlight-emitting device for different applications. In general, lightextraction relates to device efficiency, since any light generated bythe device which is not extracted can result in decreased efficiency.Light collimation can be of importance if an application thatincorporates the light-emitting device operates more efficiently, and/orwith fewer optical components, as a result of the collimated lightemission. Azimuthal isotropy may be of significance in applicationswhere isotropic light emission is desired, and where isotropic lightemission may reduce or eliminate the need for additional opticalcomponents.

As such, in many applications, it can be desirable to tailor lightextraction, collimation, and/or azimuthal isotropy.

SUMMARY OF INVENTION

In some embodiments, the invention provides devices, such aslight-emitting devices, as well as related components, systems andmethods.

In one embodiment, a light-emitting device comprises an interfacethrough which emitted light passes therethrough. The interface having adielectric function that varies spatially according to a pattern, andthe pattern arranged to provide light emission that has a substantiallyisotropic emission pattern and is more collimated than a Lambertiandistribution of light.

Other aspects, embodiments and features of the invention will becomeapparent from the following detailed description of the invention whenconsidered in conjunction with the accompanying drawings. Theaccompanying figures are schematic and are not intended to be drawn toscale. In the figures, each identical, or substantially similarcomponent that is illustrated in various figures is represented by asingle numeral or notation.

For purposes of clarity, not every component is labeled in every figure.Nor is every component of each embodiment of the invention shown whereillustration is not necessary to allow those of ordinary skill in theart to understand the invention. All patent applications and patentsincorporated herein by reference are incorporated by reference in theirentirety. In case of conflict, the present specification, includingdefinitions, will control.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic of a representative LED according to someembodiments of the invention;

FIG. 2 a is a schematic of a solid angle collection cone;

FIG. 2 b is a schematic of a collection shape defined by a correspondingset of planes;

FIG. 3 is a pattern formed by a hexagonal array of features;

FIG. 4 is an illustration of an angular displacement transformationaccording to some embodiments of the invention;

FIGS. 5 a-b are patterns generated by an angular displacementtransformation of a precursor pattern according to some embodiments ofthe invention;

FIG. 6 is a schematic representation of a transformed pattern, fromwhich portions may be selected, according to some embodiments of theinvention;

FIG. 7 is a rotated patchwork pattern according to some embodiments ofthe invention;

FIGS. 8 a-d are patterns having extended gap regions according to someembodiments of the invention;

FIG. 9 a is a hexagonal pattern;

FIG. 9 b-c are patterns generated by scaling according to someembodiments of the invention;

FIG. 10 is a pattern that includes a plurality of regions with aspecific pattern according to some embodiments of the invention;

FIG. 11 a is an illustration of a simulated emission pattern that isboth collimated and substantially uniform according to some embodimentsof the invention;

FIG. 11 b is an illustration of a simulated emission pattern that iscollimated along one axis and non-collimated along another axisaccording to some embodiments of the invention;

FIG. 12 is a schematic of an edge-illuminated light panel according tosome embodiments of the invention;

FIG. 13 a is a view of the LEDs in the edge-illuminated light panel ofFIG. 12 according to some embodiments of the invention;

FIG. 13 b is a schematic of light emission from the array of LEDs in theedge-illuminated light panel of FIG. 12 according to some embodiments ofthe invention;

FIG. 14 a-c are simulation results from a working example according tosome embodiments of the invention;

FIG. 15 a-c are simulation results from a working example according tosome embodiments of the invention;

FIG. 16 a-c are simulation results from a working example according tosome embodiments of the invention;

FIG. 17 a-d are simulation results from a working example according tosome embodiments of the invention;

FIG. 17 e-g are collection planes which can be used to characterizeanisotropic light emission according to some embodiments of theinvention; and

FIG. 18 a-b are simulation results from a working example according tosome embodiments of the invention.

DETAILED DESCRIPTION

Certain embodiments of the invention provide light-emitting devices andmethods associated with such devices. The devices may include a patternformed on an interface through which light passes through. For example,the interface can be an emission surface of the device, or an interfacebetween layers within the device. As described further below, thepattern can be defined by a series of features having certaincharacteristics (e.g., feature size, depth, nearest neighbor distances)which may be configured to influence the characteristics of the lightemitted from the device including, but not limited to, light extraction,collimation, and/or isotropy.

FIG. 1 illustrates a representative LED 100, which is an example of alight-emitting device shown for illustrative purposes. It should beunderstood that various embodiments can also be applied to otherdevices, and are not limited to just LEDs. The LED comprises amulti-layer stack 111 that may be disposed on a sub-mount (not shown).The multi-layer stack 111 can include an active region 114 which isformed between n-doped layer(s) 115 and p-doped layer(s) 113. The stackalso includes a conductive layer 112. An n-side contact pad 116 isdisposed on layer 115, and a p-side contact pad 117 may be disposed onconductive layer 112. It should be appreciated that the LED is notlimited to the configuration shown in FIG. 1, for example, the n-dopedand p-doped sides may be interchanged so as to form a LED having ap-doped region in contact with the contact pad 116 and an n-doped regionin contact with the contact pad 117. As described further below,electrical potential may be applied to the contact pads which can resultin light generation within active region 114 and emission of at leastsome of the light generated through an emission surface 118. Asdescribed further below, openings 119 may be defined in the emissionsurface, and/or at any other interface, to form a pattern that caninfluence light emission characteristics, such as extraction,collimation, and/or isotropy.

It should be appreciated that various modifications of LED 100 arepossible. For example, in one variation, electrode 117 is absent, andelectrical contact to layer(s) 113 is made via conductive layer 112through a conductive submount (not shown) which is attached toconductive layer 112. It should be understood that other variousmodifications can be made to the representative LED structure presented,and that the invention is not limited in this respect.

The active region of an LED can include one or more quantum wellssurrounded by barrier layers. The quantum well structure may be definedby a semiconductor material layer (e.g., in a single quantum well), ormore than one semiconductor material layers (e.g., in multiple quantumwells), with a smaller band gap as compared to the barrier layers.Suitable semiconductor material layers for the quantum well structuresinclude InGaN, AlGaN, GaN and combinations of these layers (e.g.,alternating InGaN/GaN layers, where a GaN layer serves as a barrierlayer).

The n-doped layer(s) 115 can include a silicon-doped GaN layer (e.g.,having a thickness of about 300 nm thick) and/or the p-doped layer(s)113 include a magnesium-doped GaN layer (e.g., having a thickness ofabout 40 nm thick). The conductive layer 112 may be a silver layer(e.g., having a thickness of about 100 nm), which may also serve as areflective layer (e.g., that reflects upwards any downward propagatinglight generated by the active region 114). Furthermore, although notshown, other layers may also be included in the LED; for example, anAlGaN layer may be disposed between the active region 114 and thep-doped layer(s) 113. It should be understood that compositions otherthan those described herein may also be suitable for the layers of theLED.

As a result of openings 119, emission surface 118 of the LED can have adielectric function that varies spatially according to a pattern whichcan influence the extraction efficiency, collimation, and/or isotropy oflight emitted by the LED. In the illustrative LED 100, the pattern isformed of openings, but it should be appreciated that the variation ofthe dielectric function at an interface need not necessarily result fromopenings.

Any suitable way of producing a variation in dielectric functionaccording to a pattern may be used. For example, the pattern may beformed by varying the composition of layer 115 and/or emission surface118. The pattern may be periodic (e.g., having a simple repeat cell, orhaving a complex repeat super-cell), periodic with de-tuning, ornon-periodic. As referred to herein, a complex periodic pattern is apattern that has more than one feature in each unit cell that repeats ina periodic fashion. Examples of complex periodic patterns includehoneycomb patterns, honeycomb base patterns, (2×2) base patterns, ringpatterns, and Archimidean patterns. As discussed below, in someembodiments, a complex periodic pattern can have certain openings withone diameter and other openings with a smaller diameter. As referred toherein, a non-periodic pattern is a pattern that has no translationalsymmetry over a unit cell that has a length that is at least 50 timesthe peak wavelength of light generated by active region 114. Examples ofnon-periodic patterns include aperiodic patterns, quasi-crystallinepatterns, Robinson patterns, and Amman patterns.

In certain embodiments, an interface of a light-emitting device ispatterned with openings which can form a photonic lattice. Suitable LEDshaving a dielectric function that varies spatially (e.g., a photoniclattice) have been described in, for example, U.S. Pat. No. 6,831,302B2, entitled-“Light Emitting Devices with Improved ExtractionEfficiency,” filed on Nov. 26, 2003, which is herein incorporated byreference in its entirety. As described further below, the pattern mayconform to a transformation of a precursor pattern according to amathematical function, including, but not limited to an angulardisplacement transformation. The pattern may also include a portion of atransformed pattern, including, but not limited to, a pattern thatconforms to an angular displacement transformation. The pattern can alsoinclude regions having patterns that are related to each other by arotation.

Light may be generated by LED 100 as follows. The p-side contact pad 117(or conductive layer 112) can be held at a positive potential relativeto the n-side contact pad 116, which causes electrical current to beinjected into the LED. As the electrical current passes through theactive region, electrons from n-doped layer(s) 115 can combine in theactive region with holes from p-doped layer(s) 113, which can cause theactive region to generate light. The active region can contain amultitude of point dipole radiation sources that generate light with aspectrum of wavelengths characteristic of the material from which theactive region is formed. For InGaN/GaN quantum wells, the spectrum ofwavelengths of light generated by the light-generating region can have apeak wavelength of about 445 nanometers (nm) and a full width at halfmaximum (FWHM) of about 30 nm, which is perceived by human eyes as bluelight. The light emitted by the LED may be influenced by any patternedinterface (e.g., the emission surface 118) through which light passes,whereby the pattern can be arranged so as to influence the collimationand/or isotropy of the emitted light.

It should be appreciated that the patterns presented herein may also beincorporated into light-collection devices, including, but not limitedto, optical filters, solar cells, and photodetectors. In such devices,the patterns may be configured to influence the collection of light bythe device including controlling collection efficiency, collectioncollimation, and/or collection isotropy. In such devices, tailoring ofthe collection collimation and isotropy can enable to collection of morelight that impinges on the collection surface with specificorientations. For example, a high collection collimation enables thedevice to collect light that is impinging on the collection surface withorientations that do not significantly deviate from the emission surfacenormal, while at the same time, collecting less of the light thatimpinges on the collection surface with orientations that significantlydeviate from the emission surface normal. Anisotropy further allows thecollection to be enhanced along one or more directions (along thecollection surface). Furthermore, the wavelength(s) of the collectedlight may also be tailored based on the pattern characteristics, forexample the nearest neighbor distance between features of the pattern.Therefore, although the embodiments that follow are described in thecontext of light-emitting devices, it should be appreciated that theinvention is not limited in this respect. For instance, the structuresdescribed herein can also be incorporated into light-collection devices,as previously described.

The schematic representation of the LED 100 illustrates angles θ and φthat can be used to characterize light emission from the emissionsurface 118. Light emission from the emission surface can becharacterized by a light emission field, where the direction of thelight emission field at any point corresponds to the direction ofpropagation of the emitted light at that point.

A light emission pattern can in turn be defined by the spatialdistribution of the light intensity emanating from the light-emittingdevice. From a calculation standpoint, the light intensity at a point inspace can be determined by the magnitude of the light emission field. Alight emission pattern can be used to determine the projection of lightonto a projection plane, or any other desired surface. Such a procedurecan be useful for calculating an emission pattern of light onto aprojection plane, where the projection plane is typically parallel tothe emission surface. For example, the projection plane may be a planeparallel to the emission surface, and for example, can be located at afar-field distance from the emission surface so as to capture thefar-field emission pattern. In embodiments presented herein, an emissionpattern refers to an intensity pattern on a projection planesubstantially parallel to the emission surface. In instances where theemission surface is not parallel to the active layer (e.g., a quantumwell), the emission pattern can refer to an intensity pattern on aprojection plane substantially parallel to the active layer.

To facilitate a description of collimation and/or isotropy of emittedlight, suitable coordinate systems may be employed. In a sphericalcoordinate system, an emission vector 102 can be defined by a polarangle θ between a normal of the emission surface and the emissionvector, and by an azimuthal angle φ on a plane defined by the emissionsurface. The definition of these angles can facilitate a description ofthe collimation and isotropy of the emitted light. In such a sphericalcoordinate system, collimation is a measure of the polar angularvariation of the light emission. Azimuthal isotropy is a measure of theisotropy of the light emission versus the azimuthal angle, hereafterreferred to simply as isotropy. In a mathematical sense, the azimuthalisotropy can be related to the variation of the emitted light intensityversus the azimuthal angle, for a constant polar angle.

The emission pattern, and hence collimation and/or isotropy of theemitted light, may be characterized based on collection shapes orsurfaces within which, or on which, emitted light can be integrated soas to determine the total light emission within, or on, that collectionshape. Some examples of collection shapes include a solid anglecollection cone, a collection plane, or sets of collection planes, butother collection shapes are also possible.

FIG. 2 a illustrates a solid angle collection cone 200 a defined by apolar angle θ_(c), referred to as a collection angle, with respect to anormal 220 of the emission surface (not shown). A solid angle cone witha specified collection angle can be used to characterize the collimationof the emitted light. The total intensity of light collected within thesolid angle cone can provide a measure of collimation. In someembodiments, the collection angle used to characterize the degree ofcollimation is greater than or equal to about 20 degrees and less thanor equal to about 45 degrees, for example, the collection angle may be30 degrees.

The variation of the total intensity of light collected within the solidangle cone as a function of the collection angle θ_(c) can be comparedto a Lambertian distribution exhibited by light-emitting devices notpossessing any surface patterns, or other features, that modify lightemission. It should also be appreciated that the variation of the lightemission as a function of the azimuthal angle may be used tocharacterize the anisotropy of the light emission.

Other collection shapes may be utilized to facilitate the description ofanisotropic light emission. In some instances, a suitable collectionshape may be a set of planes having angles θ_(c) and −θ_(c) with respectto the emission surface normal 220, and containing a common line 230which lies on the emission surface (not shown), as illustrated in FIG. 2b. To characterize anisotropy using such a collection shape, a firstintegrated collection intensity versus the collection angle can beobtained for a first orientation of line 230 on the emission surface(e.g., line 230 along an x or y axis). Then, a second integratedcollection intensity versus the collection angle can also be obtainedfor a perpendicular orientation of line 230. In this way, a measure oflight emission collimation in different emission directions may beobtained, which can therefore provide an indication of the anisotropy ofthe emission. It should be appreciated that the previously describedcollection shapes are merely some examples of collection shapes that maybe used to characterize the collimation and/or isotropy (or anisotropy)of light emitted from a light-emitting device, and that the embodimentspresented herein are not limited in this respect.

In some embodiments, a pattern on an interface of a light-emittingdevice can be used to tailor the collimation and/or isotropy of theemitted light. The pattern on the interface of the light-emitting devicecan influence the emission of light so as to generate substantiallyisotropic collimated emission. In other embodiments, the pattern on aninterface of a light-emitting device may influence the emission of lightso as to generate anisotropic light emission. The light emission may becollimated along a first axis (on the emission surface) andnon-collimated along a second axis (also on the emission surface). Insome embodiments, the first axis is perpendicular to the second axis.

Patterns that can facilitate the tailoring of light emission may conformto various arrangements of features (e.g., at an interface, such as onan emission surface). In some embodiments, the arrangement of thefeatures may be chosen based on a various techniques, as described indetail below. A pattern that has been incorporated at an interfacewithin a light-emitting device is shown in FIG. 3. The pattern 300comprises a hexagonal array of features 319 (e.g., openings) arranged toconform to a hexagonal lattice. Such a pattern may be used as a startingpattern (hereafter referred to as a precursor pattern) so as to generateother patterns based on various methods that shall be further describedbelow. Although the hexagonal precursor pattern shall be used toillustrate various embodiments, other precursor patterns may also beemployed, including any other periodic or non-periodic pattern.

In various embodiments, a pattern can be generated by transforming aprecursor pattern according to a mathematical function. It should beunderstood that, as used herein, a mathematical function does notinclude random operations. Any suitable mathematical function can beused. For example, the mathematical function may be expressed as afunction f(x):x→x′ that depends on a position vector x and generates aposition vector x′, where the position vectors belong to the space thatthe precursor pattern spans. In one embodiment, the transformation ofthe precursor pattern may be defined by mathematical function thatdepends on the radius from a specified origin on a surface (e.g., plane)containing the precursor pattern. In one embodiment, the transformationof the precursor pattern can include providing an angular displacementto features of the precursor pattern, wherein the angular displacementmay be given by a mathematical function that depends on the radialdistance of the features of the precursor pattern with respect to areference origin, as can be described by a function f(r), where r is theradial distance. In one embodiment, the transformation of the precursorpattern may be defined by a mathematical function that can dependsinusoidally on a distance from a reference axis on the plane containingthe precursor pattern (e.g., where the distance may be an x or ycoordinate value), as can be described by a function f(x) includingsin(x) and/or sin(y) factor(s) and/or terms.

The precursor pattern is an initial pattern that need not have anyphysical manifestation and that may be transformed so as to generate apattern, also referred to as a transformed pattern. In some embodiments,the precursor pattern may be periodic (e.g., having a simple repeatcell, or having a complex repeat super-cell), periodic with de-tuning,or non-periodic. Examples of periodic patterns include rectangularpatterns and hexagonal patterns. Examples of non-periodic patternsinclude quasi-crystal patterns, for example, quasi-crystal patternshaving 8-fold symmetry. The transformation of the precursor pattern maycomprise transforming the location of features that form the precursorpattern so as to generate a transformed pattern having different featurelocations. In some embodiments, the feature locations of the transformedpattern are not simply related to the precursor pattern featurelocations based on only a translation and/or rotation.

In some embodiments, the precursor pattern may be defined by featuresthat lie on a two-dimensional plane, and which may be transformed so asto generate a transformed pattern having features that lie on the sametwo-dimensional plane. The transformation may be defined by amathematical function that depends on positions on the two-dimensionalplane. The mathematical function can be represented in any number ofsuitable coordinate systems, including, but not limited to, a Cartesiancoordinate system (having coordinates x and y) or a polar coordinatesystem (having coordinates r and φ). Examples of mathematical functionsthat can be used for the transformation include an angular displacementthat at least depends on a radial distance from a reference origin,sinusoidal functions that depend on a distance from a reference axis(e.g., the x or y axis on the two-dimensional plane), scaling functionsthat depend on a position along a reference axis (e.g., elongation orcompression along an x or y axis), or combinations thereof. It should beappreciated that these are just a few examples of suitable mathematicalfunctions that may be used to accomplish the transformation of theprecursor pattern, and other suitable mathematical function may also beused.

The precursor pattern may be transformed via the transformation of thefeature positions of the precursor pattern. In one embodiment, a pointwithin each feature is transformed but the shape and orientation of thefeatures remains invariant. In another embodiment, all points withineach feature are transformed, therefore resulting in a transformation ofthe shape and orientation of each feature.

In some embodiments, a pattern conforms to a transformation of aprecursor pattern, wherein the transformation comprises an angulardisplacement transformation. For example, a mathematical transformationcan be applied to a precursor pattern to create a twist of the precursorpattern. Such a transformation can be applied such that a displacementangle is applied to each feature of the precursor pattern where thedisplacement angle may be a function of a distance to a chosen centerpoint, or reference origin, on a precursor pattern.

A schematic showing how an angular displacement transformation can beapplied to a precursor pattern is show in FIG. 4, where φ is an angulardisplacement and r is the radial distance from a chosen center feature410. In the illustration, a feature point 420 of the precursor patternis rotated by the angle φ, so as to transform the location of thefeature 420 to location 425. The angular displacement φ can have adesired variation (or lack thereof) as a function of position. Forexample, the angular displacement φ can be constant for all features, orthe angular displacement can vary as a function of a distance r from thereference origin 610 and/or x, y coordinates with respect to referenceorigin 610. In general, a local deformation of a precursor pattern canbe defined as

${a = {r\frac{\mathbb{d}{\phi(r)}}{\mathbb{d}r}\Delta\; r}},$where “a” represents a circumferential displacement of a feature pointwith respect to the chosen center point from which the radius r ismeasured.

An example of a constant angle angular displacement transformation isgiven bya=rdφ=const→φ(r)˜ln(r),where the transformed feature points experience the same circumferentialdisplacement with respect to the chosen center point.

An example of an equal angle displacement transformation may be given by

2π∫₀¹r ϕ(r)𝕕r = π/2− > ϕ(r) ∼ r²,where r=0 at the chosen center of the pattern and r=1 at the edge of thepattern. In this way, the transformation can also depend on the patternsize.

In some embodiments, an angular displacement transformation can have anytype of functional dependence on the radius r. A general classificationfor angular displacement transformations that depend on the radialdistance to a reference origin can be given by φ˜T(r), where T(r) is atransformation function which varies with the radius r from thereference origin. Examples of such transformations include

${\left. {\phi(r)}\; \right.\sim\;\sqrt[{n + r}]{r}}\mspace{14mu}\text{and}$${{\left. {\phi(r)}\; \right.\sim\;\sqrt[n]{r}},}\mspace{11mu}$where n is a constant.

An illustrative embodiment of such a pattern generated by an angulardisplacement transformation of a precursor pattern is shown in FIG. 5 a,where the mathematical function used for the transformation was given by

$\left. \phi\; \right.\sim\;\sqrt[8]{r}$and the reference origin (not shown) lies in the center of the pattern,thereby generating a twist of the precursor pattern. In this example,the precursor pattern was a periodic hexagonal pattern, but it should beappreciated that other precursor patterns may also be used, aspreviously described. For example, some other periodic precursorpatterns that may be utilized include a square pattern or a rectangularpattern. Furthermore, non-periodic patterns may also be used asprecursor patterns. In addition, although the pattern in theillustrative embodiment shown in FIG. 5 a was formed using an angulardisplacement transformation according to a mathematical function

${\left. \phi\; \right.\sim\;\sqrt[8]{r}},$other angular displacement transformations can be used.

In some embodiments, a pattern may include one or more portions of atransformed pattern conforming to a transformation of a precursorpattern. For example, the transformation may be an angular displacementtransformation of a precursor pattern, as discussed above. The patternmay comprise a plurality of cells, where each cell includes a portion ofan angular displacement transformation of a precursor pattern. The cellscan include the same portion or different portions of the transformedpattern, and can be arranged in a periodic or non-periodic arrangement.

An illustrative embodiment of a portion of an angular displacementtransformation of a precursor pattern is shown in FIG. 5 b, where themathematical function used for the transformation was given by φ=ln(r)and the reference origin lies off the illustrated pattern portion. Inthis instance, the precursor pattern was a periodic hexagonal pattern,but as previously stated, other precursor patterns may be utilized.

To further explain a method by which portions of a transformed patternmay be generated, FIG. 6 illustrates a schematic representation of atransformed pattern 610, from which portions 610, 620, and 630 may beselected. In one embodiment, the transformed pattern 610 conforms to anangular displacement transformation of a hexagonal precursor pattern,where the transformation was given by φ=ln(r). The specific patternportions 610, 620, and 630 that are illustrated in FIG. 6 correspond toportions of the aforementioned transformation of a hexagonal precursor.A new pattern can be created by arraying a selected pattern portion(e.g., 610, 620, or 630) in a periodic or non-periodic fashion. Forexample, cells including any of the portions can be arranged in an array(e.g., a rectangular array) so as to form a periodic complex-cellpattern. In other instances, more than one selected portion may bearranged in any desired configuration.

In some embodiments, a pattern can comprise a plurality of regions eachhaving a pattern related to the pattern in one of the other regions by arotation. Such patterns may be referred to as rotated patchworkpatterns. Each of the regions can be referred to as cells, and the cellscan have any shape and be arranged in any desired manner. Possibleshapes for the cells include triangles, squares, rectangles, hexagons,or even irregular shapes. The cells can have any desired size, and neednot necessarily all have the same size. The pattern within each cell maybe any pattern, including non-periodic and periodic patterns, includingbut not limited to hexagonal or rectangular patterns.

FIG. 7 illustrates a rotated patchwork pattern 700 including multiplecells that each include a rotated portion of a hexagonal pattern. Themultiple cells 701, 702, 703, and 704 are rotated with respect to oneanother by specific angles. The angle of rotation is 0 degrees for cell701, 15 degrees to the right for cell 702, 15 degrees to the left forcell 703, and 90 degrees for cell 704.

Multiple cells and rotations are possible. In some embodiments, therotation of the cells can vary randomly with respect to the adjacentcells. In other embodiments, the rotation of the cells can varyaccording to a desired rotation angle. For example, each cell could berotated 15 degrees with respect to an adjacent cell. In addition variouscell sizes can be used. Exemplary cell lengths (and/or widths) includeabout 5 microns, about 10 microns, about 25 microns, about 50 microns,about 100 microns, and about 200 microns. In some embodiments, cells canhave areas greater than about 100 microns² (e.g., 10×10 microns) and/orless than about 40000 microns² (e.g., 200×200 microns). In oneembodiment, cells have and area of about 1000 microns² (e.g., 33×33microns).

Furthermore, the cells need not necessarily be contiguous and may beseparated by regions having other patterns, or no patterning at all.Also, it should be appreciated that the cells may have patterns relatedby more than just a rotation. For example, some cells may have patternsthat are both rotated and further transformed in some other manner,including, but not limited to, scaling such a compression and/orelongation along one of more axes.

In some embodiments, a pattern includes extended gap regions in one ormore directions. Within the extended gap regions, pattern features maybe absent and/or may have altered characteristics (e.g., feature sizes)so as to differentiate the extended gap regions from other regions ofthe pattern. In some embodiments, rows and/or columns of features may beabsent from a pattern at selected locations. The extended gaps may beseparated by a desired distance or number of features.

FIGS. 8 a-d illustrate various hexagonal patterns having extended gapregions. It should be appreciated that although these patterns are basedon a hexagonal pattern of features, any other periodic or non-periodicpattern may be modified via the incorporation of similar extended gaps.FIG. 8 a illustrates a hexagonal pattern having extended gaps 800 acomprising rows of missing features. FIG. 8 b illustrates a hexagonalpattern having extended gaps 800 b comprising columns of missingfeatures. FIGS. 8 c-d illustrate hexagonal patterns where extended gapsare formed by a modification of the feature characteristics within theextended gap regions. In particular, FIG. 8 c illustrates a hexagonalpattern having extended gaps 800 c comprising columns of features havingsmaller sizes (e.g., diameters) than features in the other regions ofthe pattern. FIG. 8 d illustrates a hexagonal pattern having extendedgaps 800 d comprising columns wherein the features meld together, whichmay be viewed as the features having larger sizes (e.g., diameters) thantheir nearest neighbor distance. These are just some examples thatillustrate ways by which extended gaps may be formed given a startingpattern.

In some embodiments, a pattern may be spatially compressed along onedirection and/or spatially elongated along another direction. Elongationand/or compression (also referred to generally as scaling) of patternsalong one or more directions may enable the generation of anisotropicpatterns. An example of an elongation or compression transformationalong the x-axis and/or y-axis may be defined mathematically accordingto a function f(x=(x,y))=(k_(x) x, k_(y) y), where k_(x) and k_(y) arescaling factors along the x and y directions, respectively. Forcompression, the scaling factor is less than 1, and for elongation, thescaling factor is greater than 1. It should be appreciated scaling canbe performed along any desired axis, and need not just be performedalong the x and/or y axis. FIGS. 9 b-c illustrate examples of patternsthat conform to the elongation and/or compression of a hexagonal pattern900 a shown in FIG. 9 a. FIG. 9 b illustrates a pattern 900 b thatconforms to the compression along the y direction of hexagonal pattern900 a. FIG. 9 c illustrates a pattern 900 c that conforms to compressionalong the x direction. In another embodiment, a pattern can conform tothe compression of a precursor pattern along a first direction, and anelongation of a precursor pattern along a second direction. The firstand the second directions can be perpendicular, but need not necessarilybe so. Using such methods, patterns can be generated that haveanisotropic features and nearest neighbor distances. Some variationsinclude the introduction of compression and/or elongation for only thefeatures and/or the locations of the features.

In some embodiments, a pattern can comprise a plurality of regions,wherein each region can include a specific pattern. For example, regionsof a pattern may include any of the patterns mentioned herein, but canalso include any other pattern. FIG. 10 illustrates such an embodiment,where the pattern 1000 comprises three regions 1010, 1020, and 1030.Regions 1010 and 1030 are regions with a pattern that includes extendedgaps, whereas center region 1020 includes a hexagonal pattern withoutany missing features. Other variations of such an embodiment arepossible, where any other patterns may be used in various regions.

Once a pattern is generated, it may be incorporated into a variety ofdevices, including, but not limited to, light-emitting devices andlight-collection devices. In one embodiment, a pattern may beincorporated into a device such that an interface (e.g., an emissionsurface and/or buried interface) of the device has a dielectric functionthat varies spatially according to a transformed pattern. The variationin the dielectric function may be accomplished by a variety of means,including but not limited to incorporating openings (or protrusions) inlocations where a pattern feature should be located. In someembodiments, the pattern may lie at an interface between two materiallayers.

As previously mentioned, patterned interfaces in light-emitting (andlight-collection) devices can be used to tailor the light emissionprofile of such devices. The pattern can influence the collimation andisotropy of the light emission. In instances where a pattern is absent,the emission profile of a light-emitting device (without any collectionoptics) is known to have a Lambertian distribution dependent on thecollection angle from the emission normal. In contrast, in someembodiments presented herein, the dielectric function of an interface ofa light-emitting device varies spatially according to a pattern, and thepattern is arranged so that light generated within the light-emittingdevice emerges with an emission profile that is more collimated than aLambertian distribution. In some embodiments, a pattern can enable thetailoring of light emission so that the emission is both collimated andisotropic. As described herein, the degree of collimation may be definedin relation to a Lambertian emission distribution. Light emission can beconsidered collimated when the intensity of the emitted light at adirection normal (i.e., zero collection angle) to the emission surfaceis at least about 20% greater (e.g., at least about 30% greater, atleast about 50% greater, at least about 100% greater) than a Lambertianemission at a direction normal to the emission interface.

FIG. 11 a illustrates a simulated emission pattern that is bothcollimated and substantially isotropic, where light regions correspondto areas of higher emission intensity. Various patterns can be used toprovide such collimated isotropic emission, including, but not limitedto, the patterns illustrated in FIG. 5 a and FIG. 7. In someembodiments, a pattern that conforms to an angular displacementtransformation of a precursor pattern can be used to pattern theemission surface of a light-emitting device to provide for lightemission that is both collimated and substantially isotropic. In otherembodiments, a rotated patchwork pattern may be used to provide forlight emission that is both collimated and substantially isotropic. Asdescribed herein, a substantially isotropic emission may be defined suchthat an integrated intensity varies by less than about 20% (e.g., lessthan about 10%, less than about 5%) over all azimuthal angles, whereinthe integrated intensity is a summed intensity over all polar collectionangles.

Furthermore, in other embodiments, a pattern can enable the tailoring ofthe light emission in one or more directions to create a partiallycollimated beam. In some embodiments, a pattern can be configured so asto generate anisotropic light emission. The anisotropic light emissionmay be characterized by an emission pattern on a far-field projectionplane substantially parallel to the interface, wherein a first totallight intensity along a first axis (e.g., x-axis or y-axis) on theprojection plane is at least 20% greater than a second total lightintensity along a second axis (e.g., y-axis or x-axis) on the projectionplane. In some embodiments, the second axis is perpendicular to thefirst axis, and in further embodiments, the first total light intensityalong the first axis is at least 50% greater (e.g., at least 75%greater, at least 100% greater) than the second total light intensityalong the second axis. FIG. 11 b illustrates a simulated anisotropicemission pattern that is collimated along one axis and non-collimated(e.g., Lambertian) along the other axis. Various patterns can be used toaccomplish such partially collimated anisotropic emission, including,but not limited to, the patterns illustrated in FIG. 5 b and FIGS. 8a-d. In some embodiments, a pattern that conforms to a portion ofangular displacement transformation of a precursor pattern can be usedto pattern the emission surface of a light-emitting device, wherein theresulting light emission is anisotropic and collimated along a desiredaxis. In other embodiments, a pattern having extended gaps may result inemission that is anisotropic and collimated along a desired axis.

It is believed that a patterned light projection profile may begenerated using a light-emitting device with a surface having multiplepatterns which are spatially separate from one another. Both collimatingand non-collimating patterns can be sectioned together. An example ofsuch an embodiment is shown in FIG. 10, where the pattern consists of acenter region that can provide for highly collimated emission, and theedge pattern regions that can provide for anisotropic emission. Otherarrangements are possible depending on the desired projection pattern.

Various devices (e.g., light-emitting devices, light-collection devices)incorporating patterns, such as those described above, can be used invarious components and systems. Light-emitting devices having partiallycollimated anisotropic emission may be incorporated into components andsystems that may be suited for anisotropic emission profiles, includingbut not limited to, applications such as edge illumination of a lightpanel (e.g., for use in an LCD display or for general illumination),rear projection televisions, and far-field manipulation for projectionapplications (e.g., decorative lighting, automotive headlamps).

FIGS. 12 and 13 a-b illustrate an embodiment of an edge-illuminatedlight panel (e.g., in an LCD assembly, where an LCD layer is disposedover an illumination panel) including LEDs having partially collimatedanisotropic emission. Such partially collimated light output canincrease the coupling of the light emitted from LEDs 2216 a, 2216 b,2216 c, and 2216 d into light panel 2212 and can also enhance the mixingand distribution of the light within the panel. A LED having a patternedsurface can generate a light distribution that is collimated along onedirection and non-collimated along a different direction, such as thesimulated emission illustrated in FIG. 11 b. Such patterns can include,but are not limited to, the patterns presented in FIGS. 5 b, 8 a-d, and9 b-c, as shall be described further below in working examples.

LEDs 2216 a, 2216 b, 2216 c, and 2216 d can be positioned along the edge2211 of light panel 2212, in a manner illustrated in the perspectiveview of FIG. 12 and the side-view of FIG. 13 a. The LEDs 2216 a, 2216 b,2216 c, and 2216 d may be arranged so as to be separated by non-lightgenerating regions 2218 a, 2218 b, and 2218 c. The LED arrangement cangenerate a light distribution that includes regions of overlapping lightprojection, schematically shown as elongated cones 2232 a, 2232 b, 2232c, and 2232 d with overlapping regions 2234 a, 2234 b, and 2234 c. Asshown in FIG. 13 b, the light distribution is more collimated than atypical Lambertian light emission in the direction parallel to thickness2224 of LCD panel 2212 (indicated by arrow 2233). The surface patterncan also enhance spreading of the light in another direction (indicatedby arrow 2235), for example, in a direction perpendicular to thethickness of the display. A LED having a surface pattern that enhancescollimation along the thickness of LCD panel 2212 and allows for adiffused distribution along the length of the LCD panel 2212 can enhancethe isotropy of the light distribution entering LCD panel 2212. Forexample, the diffused distribution can spread light from the multipleLEDs (e.g., LEDs 2216 a, 2216 b, 2216 c, and 2216 d) to reduce theeffect of the spacing or non-light generating regions (e.g., regions2218 a, 2218 b, and 2218 c) between the LEDs.

Having thus described both patterns that can be incorporated intolight-emitting devices, and systems within which such light-emittingdevices may be incorporated, it should be appreciated that suchlight-emitting devices can be formed with a variety of processes andmethods known to those in the art. Device structures described in theembodiments can be fabricated using a combination of any suitableprocessing techniques. Such processes can include thin film depositiontechniques, such as chemical vapor deposition (e.g., metal-organicchemical vapor deposition), for depositing various materials, includingsemiconductors, insulators, and metals. Evaporation and sputtering canbe utilized to deposit metals. Patterning processes, such asphoto-lithography and nano-imprint techniques, may be used to form thesurface patterns described herein. Etching processes, such as dryetching (e.g., reactive ion etching), and wet etching, may be used topattern layers. Coating and spin-coating can be used to depositencapsulants. Wafer bonding processes may be used to transfer structuresand devices. Furthermore, packaging processes may be used to package theaforementioned light-emitting devices and structures.

Patterns which can enable a tailoring of the collimation and/or isotropyof the light emission may include any of the types of pattern describedherein, but are not limited to just the patterns illustrated herein.Such patterns may be generated via any of the methods described herein,or by any other suitable method, including direct selection of patternfeature locations. As previously described, a pattern to be incorporatedinto a device may be generated by a transformation of a precursorpattern. Such a transformation may be performed on a computer via amathematical transformation of a set of points describing the locationsof pattern features, or by any other means, as the invention is notlimited in this respect. Once a desired pattern is generated orselected, thereby yielding a location of features, a patterning mask maybe created and used to incorporate the pattern onto a layer of a device.The patterning process for the pattern may be performed with anysuitable patterning process, including, but not limited to,photo-lithography and nano-imprint techniques.

In addition, pattern modification processes may be included in thefabrication process via techniques such as etching vias or trenches intothe surface. In other pattern modification techniques, etching vias intothe backside of the device (i.e., through a backside mirror layer) caninfluence the emission pattern (e.g., collimation and/or isotropy) ofthe light-emitting device. In other pattern modification processes,extended gaps such as those described in relation to FIGS. 8 a-8 d, canbe fabricated using pattern modification process. In some embodiments,such as for the pattern shown in FIG. 8 c, a portion of a pattern can beunder-etched such that the periodicity of the pattern on the surface ofthe device is disrupted by a group of holes having a smaller diameter incomparison to the other holes in the pattern. In other embodiments, asshown in FIG. 8 d, a portion of the pattern can be over-etched such thatthe periodicity of the pattern on the surface of the device is disruptedby a group of holes having a larger diameter in comparison to the otherholes in the pattern. It should be appreciated that these are only someexamples of pattern modification processes, and that other fabricationmodifications are possible so as to facilitate the fabrication ofpatterns.

Working Examples

Some working examples are presented to illustrate various simulationresults for LEDs incorporating some of the aforementioned patterns. Itshould be understood that these working examples do not limit theembodiments.

Hexagonal Pattern

Although collimated emission has been obtained in prior light-emittingdevices having patterned surfaces (e.g., with hexagonal patterns), theseemission profiles possessed an eight-fold symmetry, and were neithersubstantially isotropic nor anisotropic (e.g., having substantialcollimation along only one axis in the emission surface plane). Anexample of such LEDs having a patterned surface that can provide a lightemission profile that is more collimated than a Lambertian distributionis described in U.S. Patent Publication 2004/0207310A1 which is herebyincorporated by reference, which is based on U.S. patent applicationSer. No. 10/724,029 filed on Nov. 26, 2003.

A hexagonal pattern of holes on the emission surface of a LED has beenpreviously demonstrated to create a collimated emission. Such ahexagonal surface pattern is shown in FIG. 14 a, and a correspondingsimulated emission pattern is shown in FIG. 14 b. All simulation resultspresented herein were generated using a three-dimensionalfinite-difference time-domain (FDTD). The simulation parameters includedan emission wavelength (in air) of 520 nm, an emission FWHM of 35 nm, ahexagonal array surface pattern formed of etched holes and having alattice constant of 460 nm, hole diameters of 334 nm, hole side wallslopes of 90 deg, hole depths of 250 nm, and a hole filing ratio of 50%whereby the holes fill half of the emission surface. The LED stack usedin the simulation was formed of, from bottom to top, a silver mirror, ap-GaN region having a thickness of 100 nm, an active region having athickness of 85 nm, and a n-GaN region having a thickness of 350 nm.Unless stated otherwise, the simulation parameters for otherillustrative working examples presented herein was generated viasimulations using similar parameters, except for variations in thesurface pattern.

FIG. 14 c is a graph 1400 of the simulated light extraction from thedevice as a function of collection angle away from the surface normal,represented by data curve 1410. In these simulations, the collectionshape was a solid angle collection cone, as previously described. They-axis 1422 shown on the left side of graph 1400 is the lightextraction, wherein a value of 1.0 corresponds to 100% of the lightgenerated in the active region of the LED being extracted from the LED.The dotted line 1420 represents the profile of the extraction from a LEDgenerating a Lambertian distribution. The y-axis 1424 plotted on theright side of graph 1400 shows the collimation enhancement over theLambertian 1420, given by curve 1430.

Patchwork Pattern

In some embodiments, the surface of a light-emitting device can bepatterned to generate a substantially isotropic emission pattern whilemaintaining collimation. In one embodiment, a patchwork pattern thatgenerates a substantially isotropic emission while maintainingcollimation is shown in FIGS. 15 a-c. In the illustrated pattern of FIG.15 a, a cell size of 5.5×5.5 microns was used in a simulation of LEDemission. FIG. 15 b shows a simulated emission pattern, and FIG. 15 c isa graph 1500 of the simulated light extraction from the device as afunction of collection angle away from the surface normal, representedby data curve 1510. In this illustration, the collection shape was asolid angle collection cone. The dotted line 1520 represents the profileof the extraction from a LED with a Lambertian light emissiondistribution. The collimation enhancement over the Lambertian 1520 isgiven by curve 1530. This simulation illustrates that the surfacepattern comprising of a plurality of patterned regions related by arotation can increase the collimation as compared to a Lambertiandistribution, while at the same time facilitate the generation ofsubstantially isotropic emission, as illustrated in the emission patternof FIG. 15 b.

Angular Displacement Pattern

Angular displacement patterns can be incorporated into a LED so as tofacilitate the generation of a substantially isotropic and collimatedemission pattern. FIG. 16 a illustrates a pattern that conforms to anangular displacement transformation of a hexagonal precursor pattern,generated using an angular displacement transformation according to amathematical function

${\left. \phi\; \right.\sim\;\sqrt[8]{r}}.$FIGS. 16 b-c are corresponding simulation results for the pattern shownin FIG. 16 a. FIG. 16 b shows a simulated emission pattern, and FIG. 16c is a graph 1600 of the simulated light extraction from the device as afunction of collection angle away from the surface normal, representedby data curve 1610. In this illustration, the collection shape was asolid angle collection cone. The dotted line 1620 represents the profileof the extraction from a LED generating a Lambertian light emissiondistribution. The collimation enhancement over the Lambertian 1620 isgiven by curve 1630. The surface pattern conforming to an angulardisplacement transformation of a precursor pattern can increase thecollimation as compared to a Lambertian distribution, and at the sametime generate a substantially isotropic emission, as illustrated in theemission pattern of FIG. 16 b.

Portion of an Angular Displacement Pattern

FIG. 17 a illustrates a pattern which is a 100×100 micron portion of atransformed hexagonal pattern transformed according to the functionφ=ln(r). In particular, the pattern corresponds to portion 620 of thetransformed pattern illustrated in FIG. 6. FIGS. 17 b-d arecorresponding simulation results for the pattern shown in FIG. 17 a. Thesimulated emission pattern illustrated in FIG. 17 b shows that thepattern in FIG. 17 a provides for anisotropic emission.

To further describe such emission, a corresponding set of collectionplanes, as illustrated in FIG. 2 b, can be used as a collection shape.Simulation data in graph 1700 c of FIG. 17 c illustrates the collectedlight emission within the corresponding set of planes as a function ofcollection angle from the surface normal. Emission as a function ofcollection angle for a Lambertian emission is given by curve 1720 c.Curve 1712 c is the total emission within a corresponding set of planeswhere the common line of intersection of the planes (i.e., line 230 inFIG. 2 b) is aligned along the y-axis, as illustrated in FIG. 17 e.Curve 1714 c is the total emission within a corresponding set of planeswhere the common line of intersection of the planes (i.e., line 230 inFIG. 2 b) is aligned along the x-axis, as illustrated in FIG. 17 f.

To further illustrate the anisotropy of the emission, FIG. 17 d is agraph 1700 d of the light intensity on the collection planes as afunction of collection angle. Light intensity as a function ofcollection angle for a Lambertian emission is given by curve 1720 d.Curve 1712 d is the light intensity as a function of collection angle ona corresponding set of planes where the common line of intersection ofthe planes (i.e., line 230 in FIG. 2 b) is aligned along the y-axis.Curve 1714 d is the light intensity as a function of collection angle ona corresponding set of planes where the common line of intersection(i.e., line 230 in FIG. 2 b) is aligned along the x-axis.

As can be seen from the simulation results, the light intensitycorresponding to curve 1714 d is greater than the light intensitycorresponding to curve 1712 d for at least some collection anglesbetween about −20 and 20 degrees, but this range may be modified basedon the pattern used within the light-emitting device. It can be seenfrom the simulated total collection curve 1714 c that the totalcollected emission within collection planes having a common lineoriented along the x-axis is greater than the total collected emissionof a Lambertian distribution for almost all collection angles, andespecially for collection angles greater than about 60 degrees (e.g.,greater than 40 degrees, greater than 30 degrees, greater than 20degrees, greater than 10 degrees).

In contrast, the light intensity corresponding to curve 1712 d issimilar to the Lambertian distribution 1720 d for all collection angles.The orientation of the collection shape for curves 1712 c and 1712 dcorresponds to collection planes having a common line aligned along they-axis. It can be seen from the simulated curve 1712 c that the totalcollected emission within collection planes having a common lineoriented along the y-axis is similar to the total collected emission ofa Lambertian distribution for all collection angles. As such, thepattern of FIG. 17 a can provide for collimated emission along one axisand non-collimated (e.g., Lambertian) emission along another axis.

In some embodiments presented herein, light emission from alight-emitting device is anisotropic, such that the light intensity on acollection plane along a first axis and which is perpendicular to theemission surface (i.e., 0 degree collection angle) is at least about 20%greater (e.g., at least about 50% greater, at least about 75% greater,at least about 100% greater) than the light intensity on a collectionplane along a second axis and which is also perpendicular to theemission surface (i.e., 0 degree collection angle), where the first andsecond axis are perpendicular. In the working example of FIG. 17, basedon the simulation results shown in FIG. 17 d, the light intensity on acollection plane along the x-axis and which is perpendicular to theemission surface (i.e., 0 degree collection angle) is about 1.8 timesgreater than the light intensity along a collection plane containing they-axis and which is also perpendicular to the emission surface (i.e., 0degree collection angle). To illustrate the geometry of such collectionplanes, FIG. 17 g shows the collection planes for the 0 degreecondition, where a first plane 1740 is aligned along the x-axis, and asecond plane 1750 is aligned along the y-axis. It should be appreciatedthat these collection planes are simply geometrical constructs that maybe used to describe the light emission, in particular anisotropic lightemission.

Extended Gaps Pattern

FIG. 18 a illustrates a pattern having extended gap regions orientedalong one direction. FIG. 18 b shows the simulated anisotropic emissionresulting from the incorporation of such a pattern into a LED. Such ananisotropic pattern can be characterized using a corresponding set ofplanes oriented along different directions, such as those illustrated inFIGS. 17 e-g, or by using any other suitable method to characterize theanisotropy as the invention is not limited in this respect.

Based on the rotational symmetry of the hexagonal pattern, the simulatedemission pattern corresponding to the pattern of FIG. 18 a has someinherent asymmetry. By omitting extended sections of the pattern in onedirection, a Lambertian component can be added to the emission profilein the selected direction. FIG. 18 a shows such a pattern wherehorizontal lines of a hexagonal pattern have been deleted. The simulatedemission pattern in FIG. 18 b shows that emission is stronger along thex-axis, as compared to emission along the y-axis, which is similar tothe emission illustrated in FIG. 17 b. Omitting an increasing number offeature lines of the pattern can further increase the intensity ratiobetween emission along the x-axis and y-axis, however, total surfaceemission (i.e., extraction) from the device may decrease as more andmore of the surface pattern is deleted. A similar effect may be seen fora pattern where vertical lines of a hexagonal pattern are omitted.

Scaled Patterns

Without wishing to be bound by theory, a collimating surface patternwhere the pattern features are compressed in one direction and/orelongated along a second direction can also be used to create ananisotropic emission pattern. Furthermore, any type of pattern can bescaled accordingly to enhance the anisotropic emission pattern. Forexample, a pattern conforming to a transformation, such as an angulardisplacement transformation (e.g., of a hexagonal precursor pattern),may be compressed along a first direction and/or elongated along asecond direction.

Having thus described several aspects of at least one embodiment of thisinvention, it is to be appreciated various alterations, modifications,and improvements will readily occur to those skilled in the art. Suchalterations, modifications, and improvements are intended to be part ofthis disclosure, and are intended to be within the spirit and scope ofthe invention. Accordingly, the foregoing description and drawings areby way of example only.

1. A light-emitting device comprising: an interface through whichemitted light passes therethrough, the interface having a dielectricfunction that varies spatially according to a pattern, the patternarranged to provide light emission that has a substantially isotropicemission pattern and is more collimated than a Lambertian distributionof light, wherein the substantially isotropic emission pattern is suchthat an integrated intensity varies by less than 20% over all azimuthalangles, wherein the integrated intensity is a summed intensity over allpolar collection angles.
 2. The device of claim 1, wherein theintegrated intensity varies by less than 10% over all azimuthal angles.3. The device of claim 1, wherein a total of the emitted light within asolid angle collection cone is greater than a total emissioncorresponding to the Lambertian distribution within the solid anglecollection cone, wherein the solid angle collection cone has a centeraxis oriented along a normal of the surface.
 4. The device of claim 3,wherein the solid angle collection cone has a collection angle of 30degrees with respect to the normal of the surface.
 5. The device ofclaim 1, wherein the pattern conforms to a transformation of a precursorpattern according to a mathematical function.
 6. The device of claim 5,wherein the precursor pattern comprises a periodic pattern.
 7. Thedevice of claim 6, wherein the precursor pattern comprises a hexagonalpattern.
 8. The device of claim 5, wherein the precursor patterncomprises a non-periodic pattern.
 9. The device of claim 5, wherein themathematical function comprises providing an angular displacement thatat least depends on a radial distance from a reference origin.
 10. Thedevice of claim 5, wherein the precursor pattern comprises a pluralityof features, and wherein the transformation of a precursor pattern isapplied to positions of the plurality of features of the precursorpattern.
 11. The device of claim 1, wherein the pattern comprises aplurality of holes formed in the interface.
 12. The device of claim 1,wherein the pattern is non-periodic.
 13. The device of claim 1, whereinthe pattern comprises a first region and a second region, the firstregion having a dielectric function that varies spatially according to afirst pattern, the second region having a dielectric function thatvaries spatially according to a second pattern, the second pattern beinga rotation of the first pattern.
 14. The device of claim 13, wherein thefirst region has an area of greater than 100 microns².
 15. The device ofclaim 13, wherein the first region has an area of less than 40000microns².
 16. The device of claim 13, wherein the first pattern isperiodic.
 17. The device of claim 16, wherein the first patterncomprises a hexagonal pattern.
 18. The device of claim 13, wherein thefirst pattern is non-periodic.
 19. The device of claim 13, wherein thefirst pattern is quasi-crystalline.